A171777 E.g.f.: A(x) = exp( Sum_{n>=1} 2^(n(n-1)/2) * x^n/n ).

1, 1, 3, 23, 473, 27057, 4102027, 1539365191, 1365364095921, 2783117747148641, 12795599930746180499, 130882205973999096722679, 2946911413331842739385098377, 144807670567304192694224250060817, 15419384323650924141916096692523710747

Offset: 0

Author

Paul D. Hanna, Jan 23 2010

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 23*x^3/3! + 473*x^4/4! +...
log(A(x)) = x + 2*x^2/2 + 2^3*x^3/3 + 2^6*x^4/4 + 2^10*x^5/5 +...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..77

Crossrefs

Cf. A171776, A155200.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
      binomial(n-1, j-1)*(j-1)!*2^(j*(j-1)/2), j=1..n))
    end:
seq(a(n), n=0..14);  # Alois P. Heinz, Mar 15 2023

PARI

{a(n)=n!*polcoeff(exp(sum(m=1, n+1, 2^(m*(m-1)/2)*x^m/m)+x*O(x^n)), n)}